A began a business with Rs. 85,000. He was joined afterwards by B. With Rs. 51,000. For how much period does B join, if the profits at the end of the year are divided in the ratio of 5:1?
A .4 months
B .6 months
C .8 months
D .3 months

HINT:Proceed the solution of this question, using the concept that ratio of product of investment and time duration is equal to ratio of profit.

Complete step by step answer:
Here, in question it is given, for A, Investment (Contribution) =85000 Rs. for 1 year (12 months)
For B, investment =51000 Rs.
Let B join A for X months’ period.

Now, we know that \[\dfrac{{{\text{Investment by A}} \times {\text{ Its time duration of investment }}}}{{{\text{Investment by B}} \times {\text{ Its time duration of investment}}}} = {\text{ ratio of profit}}\]

It is given ratio of their profit =5:1
⇒\[\dfrac{{8500 \times {\text{ 12}}}}{{5100 \times {\text{ x}}}} = {\text{ }}\dfrac{5}{1}\]
On doing cross multiplication
\[ \Rightarrow 8500 \times {\text{ 12}} = {\text{ }}5 \times 5100{\text{x}}\]
On solving
\[ \Rightarrow \dfrac{{8500 \times {\text{ 12}}}}{{5 \times 5100}} = {\text{ x}}\]
⇒x ​ = 4 Months
Hence, B joined A after 12−x=12−4=8 months from the start of business and hence he joined for 4 months.

Note-In this particular question, we have to find only the ratio of profit by A and B so here we can consider the profit as a product of investment and duration of investment by anyone. Here we have